Question

An employment information service claims the mean annual pay for full-time male workers over age 25 without a high school diploma is $22,250. The annual pay for a random sample of 10 full-time male workers over age 25 without a high school diploma is listed. At α=0.01, test the claim that the mean salary is $22,250.

Assume the population is normally distributed. 20,659 21,136 22,356 21,398 22,978 16,913 19,153 23,196 24,186 26,283

What is(are) the critical value(s), t 0t0? t 0= (Use a comma to separate answers as needed. Round to three decimal places as needed.)

Answer 1

We have,

The hypothetical mean value, μ₀ = 22250

From the sample of size = 10

Mean	21825.8
Variance	6913669.2889
Stand. dev.	2629.3857

The test statistic :

d.f. = n -1

where,

= Sample mean
μ₀ = hypothetical mean value
s = Sample Standard Deviation
n = The size of the sample

After substituting these values into the formula for t we have :

  

The critical value for t with degrees of freedom = 9 and α=0.01

t₀= 3.249823

The absolute value of the calculated t is smaller than critical value (-0.5102<3.25), so the mean of data set is not significantly different from μ0=2225.